Coordination Game
In game theory, coordination games are a class of games with multiple pure strategy Nash equilibria in which players choose the same or corresponding strategies. Coordination games are a formalization of the idea of a coordination problem, which is widespread in the social sciences, including economics, meaning situations in which all parties can realize mutual gains, but only by making mutually consistent decisions. A common application is the choice of technological standards.
For a classic example of a coordination game, consider the 2-player, 2-strategy game, with the payoff matrix shown on the right (Fig. 1).
| Left | Right | |
| Up | A, a | C, c |
| Down | B, b | D, d |
| Fig. 1: 2-player coordination game | ||
If this game is a coordination game, then the following inequalities in payoffs hold for player 1 (rows): A > B, D > C, and for player 2 (columns): a > c, d > b. In this game the strategy profiles {Left, Up} and {Right, Down} are pure Nash equilibria, marked in gray. This setup can be extended for more than two strategies (strategies are usually sorted so that the Nash equilibria are in the diagonal from top left to bottom right), as well as for a game with more than two players.
Read more about Coordination Game: Examples, Mixed Nash Equilibrium, Coordination and Equilibrium Selection, Other Games With Externalities
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